管理科学03线性规划B课件

ChapterTopicsComputerSolutionSensitivityAnalysis1Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisEarlylinearprogrammingusedlengthymanualmathematicalsolutionprocedurecalledtheSimplexMethod(SeeCD-ROMModuleA).StepsoftheSimplexMethodhavebeenprogrammedinsoftwarepackagesdesignedforlinearprogrammingproblems.Manysuchpackagesavailablecurrently.Usedextensivelyinbusinessandgovernment.TextfocusesonExcelSpreadsheetsandQMforWindows.ComputerSolution2Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisBeaverCreekPotteryExampleExcelSpreadsheet–DataScreen(1of5)Exhibit3.13Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisBeaverCreekPotteryExample“Solver”ParameterScreen

(2of5)Exhibit3.24Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisExhibit3.3BeaverCreekPotteryExampleAddingModelConstraints(3of5)5Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisExhibit3.4BeaverCreekPotteryExampleSolutionScreen(4of5)6Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisBeaverCreekPotteryExampleAnswerReport(5of5)Exhibit3.57Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisLinearProgrammingProblemStandardFormStandardformrequiresallvariablesintheconstraintequationstoappearontheleftoftheinequality(orequality)andallnumericvaluestobeontheright-handside.Examples:x3x1+x2mustbeconvertedtox3-x1-x2

0x1/(x2+x3)2becomesx12(x2+x3)andthenx1-2x2-2x3

0

8Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisBeaverCreekPotteryExampleQMforWindows–DataScreen

(1of3)Exhibit3.69Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisBeaverCreekPotteryExampleModelSolutionScreen

(2of3)Exhibit3.710Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisBeaverCreekPotteryExampleGraphicalSolutionScreen

(3of3)Exhibit3.811Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisBeaverCreekPotteryExampleSensitivityAnalysis

(1of4)Sensitivityanalysisdeterminestheeffectonoptimalsolutionsofchangesinparametervaluesoftheobjectivefunctionandconstraintequations.Changesmaybereactionstoanticipateduncertaintiesintheparametersortoneworchangedinformationconcerningthemodel.12Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisMaximizeZ=$40x1+$50x2subjectto: 1x1+2x240 4x2+3x2120 x1,x20Figure3.1OptimalSolutionPointBeaverCreekPotteryExampleSensitivityAnalysis

(2of4)13Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisMaximizeZ=$100x1+$50x2subjectto: 1x1+2x240 4x2+3x2120 x1,x20Figure3.2Changingthex1ObjectiveFunctionCoefficientBeaverCreekPotteryExampleChangex1ObjectiveFunctionCoefficient(3of4)14Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisMaximizeZ=$40x1+$100x2subjectto: 1x1+2x240 4x2+3x2120 x1,x20Figure3.3Changingthex2ObjectiveFunctionCoefficientBeaverCreekPotteryExampleChangex2ObjectiveFunctionCoefficient(4of4)15Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisThesensitivityrangeforanobjectivefunctioncoefficientistherangeofvaluesoverwhichthecurrentoptimalsolutionpointwillremainoptimal.Thesensitivityrangeforthexicoefficientisdesignatedasci.ObjectiveFunctionCoefficientSensitivityRange(1of3)16Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisobjectivefunctionZ=$40x1+$50x2sensitivityrangefor: x1:25c1

66.67 x2:30c2

80Figure3.4DeterminingtheSensitivityRangeforc1ObjectiveFunctionCoefficientSensitivityRangeforc1andc2(2of3)17Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisMinimizeZ=$6x1+$3x2subjectto: 2x1+4x2

16 4x1+3x2

24 x1,x2

0sensitivityranges: 4c1

0c2

4.5ObjectiveFunctionCoefficientFertilizerCostMinimizationExample(3of3)Figure3.5FertilizerCostMinimizationExample18Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisExhibit3.9ObjectiveFunctionCoefficientRangesExcel“Solver”ResultsScreen(1of3)19Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisExhibit3.10ObjectiveFunctionCoefficientRangesBeaverCreekExampleSensitivityReport(2of3)20Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisExhibit3.11ObjectiveFunctionCoefficientRangesQMforWindowsSensitivityRangeScreen(3of3)21Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisChangesinConstraintQuantityValuesSensitivityRange(1of4)Thesensitivityrangeforaright-hand-sidevalueistherangeofvaluesoverwhichthequantityvaluescanchangewithoutchangingthesolutionvariablemix,includingslackvariables.22Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisChangesinConstraintQuantityValuesIncreasingtheLaborConstraint(2of4)MaximizeZ=$40x1+$50x2subjectto: 1x1+2x240 4x2+3x2120 x1,x20Figure3.6IncreasingtheLaborConstraintQuantity23Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisChangesinConstraintQuantityValuesSensitivityRangeforLaborConstraint(3of4)Sensitivityrangefor: 30q1

80hrFigure3.7DeterminingtheSensitivityRangeforLaborQuantity24Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisChangesinConstraintQuantityValuesSensitivityRangeforClayConstraint(4of4)Sensitivityrangefor: 60q2

160lbFigure3.8DeterminingtheSensitivityRangeforClayQuantity25Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisExhibit3.12ConstraintQuantityValueRangesbyComputerExcelSensitivityRangeforConstraints(1of2)26Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisExhibit3.13ConstraintQuantityValueRangesbyComputerQMforWindowsSensitivityRange(2of2)27Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisChangingindividualconstraintparametersAddingnewconstraintsAddingnewvariablesOtherFormsofSensitivityAnalysisTopics(1of4)28Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisOtherFormsofSensitivityAnalysisChangingaConstraintParameter(2of4)MaximizeZ=$40x1+$50x2subjectto: 1x1+2x240 4x2+3x2120 x1,x20Figure3.9Changingthex1CoefficientintheLaborConstraint29Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisAddinganewconstrainttoBeaverCreekModel: 0.20x1+0.10x2

5hoursforpackaging Originalsolution:24bowls,8mugs,$1,360profitExhibit3.13OtherFormsofSensitivityAnalysisAddingaNewConstraint(3of4)30Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisAddinganewvariabletotheBeaverCreekmodel,x3,athirdproduct,cupsMaximizeZ=$40x1+50x2+30x3subjectto:x1+2x2+1.2x3

40hroflabor4x1+3x2+2x3

120lbofclayx1,x2,x3

0Solvingmodelshowsthatchangehasnoeffectontheoriginalsolution(i.e.,themodelisnotsensitivetothischange).

OtherFormsofSensitivityAnalysisAddingaNewVariable(4of4)31Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisDefinedasthemarginalvalueofoneadditionalunitofresource.Thesensitivityrangeforaconstraintquantityvalueisalsotherangeoverwhichtheshadowpriceisvalid.ShadowPrices(DualValues)32Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisMaximizeZ=$40x1+$50x2subjectto: x1+2x2

40hroflabor 4x1+3x2

120lbofclay x1,x2

0Exhibit3.14ExcelSensitivityReportforBeaverCreekPotteryShadowPricesExample(1of2)33Chapter3-LinearProgramming:ComputerSolutionandSensitivityAnalysisExcelSensitivityReportforBeaverCreekPotterySolutionScr